Inviscid stability of compressible flows past compliant surfaces

TL;DR

This paper extends classical inviscid stability theorems to compressible flows over compliant surfaces, deriving new criteria and bounds for wave-speed and neutral modes, highlighting differences from rigid wall and incompressible cases.

Contribution

It introduces modified stability criteria and bounds for compressible flows past compliant walls, including the existence of neutral modes without critical points.

Findings

Modified inflection point criteria for compliant walls

Bounds for wave-speed of unstable modes in compressible flows

Existence of neutral modes without critical points in dissipative compliant walls

Abstract

The classical theorems of inviscid stability have been extended for compressible flows past compliant surfaces. We consider normal modes imposed on a plane parallel compressible flow past compliant walls modelled as spring-backed plates and analyze the inviscid equations to derive the theorems. We show that the generalised inflection point criteria of compressible rigid wall flows is modified for flows past dissipative compliant walls. Theorems on the bounds for the wave-speed for unstable modes in the inviscid limit are derived. These are similar to the ones for incompressible compliant wall flows, but are different from compressible rigid wall flows. A new criterion for existence of neutral modes with wave-speeds outside the range of minimum and maximum base velocities is derived for compressible flows past non-dissipative compliant walls. We show that in external compressible flows, neutral modes without a critical point can exist even with dissipative compliant walls, which is not the case in the incompressible limit.